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Theorem pm4.43 865
Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Assertion
Ref Expression
pm4.43 (𝜑 ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))

Proof of Theorem pm4.43
StepHypRef Expression
1 pm3.24 635 . . 3 ¬ (𝜓 ∧ ¬ 𝜓)
21biorfi 673 . 2 (𝜑 ↔ (𝜑 ∨ (𝜓 ∧ ¬ 𝜓)))
3 ordi 738 . 2 ((𝜑 ∨ (𝜓 ∧ ¬ 𝜓)) ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))
42, 3bitri 177 1 (𝜑 ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 101  wb 102  wo 637
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 552  ax-in2 553  ax-io 638
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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